Radix-16 Signed-Digit Division
IEEE Transactions on Computers
Computer Arithmetic: Principles, Architecture and Design
Computer Arithmetic: Principles, Architecture and Design
A variable precision processor module
A variable precision processor module
Structured arithmetic tiling of integrated circuits
Structured arithmetic tiling of integrated circuits
Constant-Time Addition and Simultaneous Format Conversion Based on Redundant Binary Representations
IEEE Transactions on Computers
Further Reducing the Redundancy of a Notation Over a Minimally Redundant Digit Set
Journal of VLSI Signal Processing Systems
New Redundant Representations of Complex Numbers and Vectors
IEEE Transactions on Computers
Digit-Set Conversions: Generalizations and Applications
IEEE Transactions on Computers
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The set theory of arithmetic decomposition is a method of designing complex addition/subtraction circuits at any radix using strictly positional, sign-local number systems. The specification of an addition circuit is simply an equation that describes the inputs and the outputs as weighted digit sets. Design is done by applying a set of rewrite rules known as decomposition operators to the equation. The order in which and weight at which each operator is applied maps directly to a physical implementation, including both multiple-level logic and connectivity. The method is readily automated, and has been used to design some higher radix arithmetic circuits. It is possible to compute the cost of a given adder before the detailed design is complete.